I am trying to use path analysis to test a model. I have one main predictor of theoretical interest (a type of personality variable), leading to a process variable, which then influences an outcome variable.

I have 7 other variables I need to control for to see if my main exogenous variable predicts over and beyond the others.

My questions are:

1) Is it common practice to use a partialled out covariance matrix to free up degrees of freedom, instead of explicitly modeling all control variables in path analysis

It is not common practice to analyze a residual matrix in my experience. It is always better to do an anlysis in one step rather than more than one. I would include that control variables in the model as covariates.